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Is there any difference? Yes. You will expose after filtration, allowing your sensor to collect the maximum amount of data. By applying a filter in post, you necessarily reduce the amount of data in your image.

Does the difference matter? Your mileage may vary. I used to take a heap of filters with me, but now I only bring a few specialized ones: circular polarizing, star, ND. I find the data loss does not impact the final image quality, so for me, bringing the extra filters is pointless. You might be an image purist, and if so, you'd want to do your filtration on the lens.

I should say, I use a UV filter mostly as plain glass to protect the lens. This debate rages on, but the difference between images shot with and without are (to my eye) negligible. A circular polarizer is much more interesting, as it actually modifies which light arrives at the sensor. Any attempt to emulate this in post processing is just that: emulation. You will always get better effects and control with the actual filter.

For major color corrections like fluorescent, you have to make the call whether letting more light in and controlling the color temperature in camera or post is better than filtering with a pretty high filter-factor piece of glass. Again, just for me, I correct on the camera and don't use the filter; I correct again in RAW conversion for the final tweaks.

I'm not sure what the question regarding special features that can be achieved with post processing means, but once you get into digital manipulation, the only limit is you imagination. So, yes, there are tons of effects that are digital only.